Here the matrix \(({\bf I}+\gamma \mathbf {X}_s\mathbf {X}_s^{\rm T})\)  in (REF ) is the resistive force theory approximation relating the hydrodynamic force along a slender filament in a Stokes (Newtonian) fluid to its velocity [1]}, [2]}, [3]}. The parameter \(\gamma \)  is a shape factor which depends on the aspect ratio of the filament; for a very slender filament, \(\gamma \approx 1\) .
